Finland was, until 1917, part of Sweden, then after 1809 of the Russian Empire. Finnish literature didn't get going until about 1880, when the national awareness movement began to make Finnish-speakers realise that their language could also be used for literary purposes. Before that time, most literature in Finland was written in Swedish.
The Wikipedia gives a good overview of Finnish literature:
Finnish literature - Wikipedia, the free encyclopedia
And by Googling the names on the list of Finlandia prizewinners, you can get a good idea of some of the more important names of poets and novelists since 1984:
Finlandia Prize - Wikipedia, the free encyclopedia
English translations are few and far between, even now that the country has about 5 million inhabitants, and companies such as Nokia are world famous, as well as more cultural matters, such as the music of Sibelius.
The best place to start to get an overview is with the quarterly magazine Books From Finland. There you can also find what is available in English translation:
Books from Finland
This magazine does review Finland-Swedish authors' works as well. But as 96% of Finland speaks Finnish, its clear focus is on literature written in the Finnish language. Their blurb:
Recent translations into English include:Published since 1967, Books from Finland is an illustrated quarterly English-language magazine about books from and about Finland.
We publish work by contemporary Finnish and Finland-Swedish writers ? poetry, prose, fiction, essays and interviews in new translations ? and articles, features and reviews of non-fiction, reflecting the scope of cultural life in the country. We also share with our readers the best choices of classic Finnish prose and poetry.
And, for Books from Finland, life is not just fiction: we also try to portray the society in which literature is born ? Finland at the beginning of the new millennium.
Books from Finland is published by the Finnish Literature Society with financial support from the Finnish Ministry of Education. We have readers in more than 80 countries, and look forward to welcoming you to experience the best Finnish literature in the world!
Anita Konkka: A Fool's Paradise, Dalkey Archive Press (trans. Haun / Witesman), 2006
Review at: A Fool's Paradise - Anita Konkka
Rosa Liksom: Dark Paradise, Dalkey Archive Press (translator: David McDuff), 2007
Review at: A review of Dark Paradise by Rosa Liksom :: The Compulsive Reader :: A Haven for Book Lovers
Marja-Liisa Vartio: The Parson's Widow, Dalkey Archive Press (trans. Aili & Austin Flint), 2008
Description at: http://www.amazon.com/Parsons-Scandinavian-Literature-Dalkey-Archive/dp/1564784835
Gunnar Bj?rling: You Go the Words, Action Books (trans. Fredrik Herzberg), 2007
Description at: Action Books - Catalog